This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This study investigated a simple model of transformers that have liquid magnetic cores
with different concentrations of ferro-nanofluids. The simple model was built on a
capillary by enamel-insulated wires and with ferro-nanofluid loaded in the capillary.
The ferro-nanofluid was fabricated by a chemical co-precipitation method. The performances
of the transformers with either air core or ferro-nanofluid at different concentrations
of nanoparticles of 0.25, 0.5, 0.75, and 1 M were measured and simulated at frequencies
ranging from 100 kHz to 100 MHz. The experimental results indicated that the inductance
and coupling coefficient of coils grew with the increment of the ferro-nanofluid concentration.
The presence of ferro-nanofluid increased resistance, yielding to the decrement of
the quality factor, owing to the phase lag between the external magnetic field and
the magnetization of the material.

Introduction

In coming decades, new generations of electronic products such as mobile phones, notebooks,
and e-paper will be developed with the primary goals of mobilization and miniaturization.
New CMOS fabrication technology will be applied to fabricate the miniaturized IC of
electronic products on silicon substrates, including on-chip micro-transformers. Several
issues of on-chip micro-transformers have been investigated for many years [1-21]. Some researches focused on the material of the magnetic core [1-10] and the geometry of the transformer [11-14]. Some papers discussed the parasitic effect of the conductive substrates. Transformer
losses become dramatic at high frequencies and limit the performance of the transformers.
Previous studies have discussed in detail the causes of transformer losses such as
parasitic capacitance, ohmic loss, and substrate loss [15-18]. Core loss from the solid magnetic core significantly affected the performance of
the transformers. The solutions for the solid magnetic core loss were proposed [19-21].

Consequently, only a few studies addressed transformers with liquid magnetic cores.
The liquid magnetic core, ferro-nanofluid, with its distinguishing features of low
electric conductivity and super-paramagnetism is regarded as a solution to the core
losses of eddy current and hysteresis. In this study, a ferro-nanofluid was applied
as a liquid magnetic core in a transformer. The performance of the transformer with
the ferro-nanofluids was measured, simulated, and compared with that of a transformer
with an air core.

Experiment

The ingredients of ferro-nanofluid used in this study were Fe3O4 nanoparticles, oleic acid, and diesel oil. The oil-based Fe3O4 nanofluid was synthesized by co-precipitation, surface modification, nanoparticles
dispersing, and base-fluid phase changing [10].

The shape and size of the Fe3O4 nanoparticles was examined by a transmission electron microscope (TEM). Figure 1 shows the TEM photo of the Fe3O4 nanoparticles. The average diameter of the nanoparticles was approximately 10 nm.
The crystalline phases of Fe3O4 nanoparticles were determined by X-ray diffraction, as shown in Figure 2. The magnetic properties of Fe3O4 nanofluid were measured by a vibrating sample magnetometer (VSM). The magnetized curve
of the Fe3O4 nanofluid measured by a VSM is shown in Figure 3. The measured results illustrate that the synthesized ferro-nanofluids have the characteristic
of super-paramagnetism. The saturated magnetizations of 0.25, 0.5, 0.75, and 1 M Fe3O4 nanofluids were 3.75, 8.85, 12.7, and 16.7 emu/g, respectively.

Figure 3.The magnetized curve of the Fe3O4 nanofluid measured by a VSM.

A liquid magnetic core of a transformer was used in this study; the capillary served
as a container in which the Fe3O4 nanofluid was loaded. The coils of the transformer were made by winding enamel-insulated
wires on a capillary. Figure 4 shows the transformer on a capillary, which loads the oil-based Fe3O4 nanofluid. The diameter of the enamel-insulated wire used was 0.45 mm, and the thickness
of the enamel layer was approximately 0.05 mm. The primary and secondary windings
had 20 turns. The outer and inner diameters of the capillary were 3.2 and 2.3 mm,
respectively, and the capacity of the capillary was 100 μL.

Figure 4.The transformer on a capillary that loads the oil-based Fe3O4 nanofluid.

Results and discussion

Different magnetic cores, air, and Fe3O4 nanofluids of 0.25, 0.5, 0.75, and 1 M were applied as the magnetic core of transformers.
The inductance (L), coupling coefficient (K), resistance (R), and quality factor (Q) were measured by an Agilent 4294A Precision Impedance Analyzer. In this study, the
simulation of the transformer was also established with HFSS 3D Full-wave Electromagnetic
Field Simulation. By applying measured permeability, permittivity, and magnetic tangent
loss and setting exciting sources, the impedances will be calculated by the finite
element method. Both the frequencies of measurement and simulation range from 100
kHz to 100 MHz.

Figure 5 shows the inductances of the coils of the transformers with different magnetic cores.
Figure 5 illustrates that the inductance grows linearly with the increase of Fe3O4 concentration. At frequencies ranging from 100 kHz to 15 MHz, the inductances decrease
rapidly due to the skin effect of coils. At frequencies ranging from 15 to 100 MHz,
the inductances increase gradually and approach the maximum inductance at the resonance
frequency. Figure 6 shows the measured and simulated results of the coupling coefficients of the transformers
with different magnetic cores. The coupling coefficients also increase with the increase
of Fe3O4 concentration. It increases rapidly below frequencies of 5 MHz and increases gradually
with frequencies over 5 MHz. These results show that the magnetic cores of nanofluids
can improve the inductance and coupling coefficients.

Figure 5.The inductances of coils of transformers with different magnetic cores.

Figure 7 shows that the resistance increases with the increase of Fe3O4 concentration, and it increases as a function of frequency. At 100 MHz, the resistances
with the magnetic core of 0.25 and 1 M Fe3O4 nanofluids were two and five times the resistance as the air core. It is speculated
that this is because of the phase lag on the material magnetization behind the external
magnetic field at high frequencies. When the relaxation times cannot keep up the alternate
time of the magnetic field, the resistance of the coils will grow rapidly [10,22]. At high frequencies, the permeability should be regarded as a complex number. Rearranging
complex permeability and the inductance of a solenoid-type inductor, the impedance
equation is obtained as follows:

Figure 7.The resistances of coils of transformers with different magnetic cores.

(1)

where ω is the angular frequency, N is the turns of coil, A is the cross-sectional area of solenoid, and l is the length of solenoid, μ" is the real part of complex permeability, and μ" is
the imaginary part of complex permeability. It can be observed that the imaginary
part of complex permeability μ" reflects on the real part of impedance, which is the
cause of increasing resistance. Then, the quality factor Q, which is defined as the ratio of inductance to resistance, becomes [10]:

(2)

Figure 8 shows the quality factor of coils of transformers with different magnetic cores.
Owing to the fact that the increase of resistance is larger and faster than that of
inductance with the presence of Fe3O4 nanofluids, the quality factor decreases when the Fe3O4 concentration rises. The simulated results show the same trend.

Conclusions

In this study, different concentrations of ferro-nanofluids were applied to the magnetic
cores of transformers. The performance of transformers with magnetic cores of air
and Fe3O4 nanofluids of 0.25, 0.5, 0.75, and 1 M were measured, simulated, and compared. The
experimental results indicated that the presence of Fe3O4 improved the inductance and the coupling coefficient of the coils. Due to phase lag
on the material magnetization behind the external magnetic field at high frequencies,
the resistance increased larger and faster than inductance, thus yielding a lower
quality factor. For a micro-transformer, if a solid magnetic core is needed for higher
inductance, it could be achieved by adding ferro-nanofluid and removing the base fluid
repeatedly. This method has a lower thermal budget than the processes that sputtered
or electroplated materials on chips. It is compatible with the MEMS process.

Abbreviations

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

TH performed experimental investigations of electric and magnetic properties of ferro-nanofluids
on transformers and prepared the draft, PH proposed the phenomena for investigation
and revised the manuscript, DS suggested the theory for the explanation of measured
results, and CT designed the experimental systems. All authors read and approved the
final manuscript.

Acknowledgements

The authors deeply appreciate the financial support provided by the National Science
Council in Taiwan under the grant numbers of NSC 96-2628-E-002-194-MY3 and NSC 98-3114-E-002-002-CC2.